Market Differences and Price Influencers Trend AnalysisAcross Cities

Introduction

Problem

Airbnb has become an increasingly popular way for travelers to find accommodations around the world. With a wide range of options available, from budget-friendly shared rooms to luxurious villas, Airbnb has something for everyone.

The intent of this data analysis report aims to identify major differences in the Airbnb market between cities and identify the attributes that have the biggest influence on price.

Data

To achieve this, we will collect data from Airbnb listings across multiple cities and perform an exploratory data analysis to identify patterns and trends in the data.

Approach/Analytic Technique

We will investigate how factors such as location, property type, amenities, and availability affect the price of Airbnb rentals in different cities. Additionally, we will identify the most influential attributes on price and provided insights and recommendations for Airbnb hosts and potential guests

How to Decide

In conclusion, we will provide insights and recommendations to Airbnb hosts and potential guests on how to optimize their listings and bookings, as well as to inform policymakers and industry stakeholders on the state of the Airbnb market across different cities.

Packages Required

The packages required to run the code in this study are the following:

library(readxl)       # To read in the data

## Warning: package 'readxl' was built under R version 4.2.2

library(tidyverse)    # For general data manipulation and regression analysis

## Warning: package 'tidyverse' was built under R version 4.2.2

## Warning: package 'ggplot2' was built under R version 4.2.2

## Warning: package 'tibble' was built under R version 4.2.2

## Warning: package 'tidyr' was built under R version 4.2.2

## Warning: package 'readr' was built under R version 4.2.2

## Warning: package 'purrr' was built under R version 4.2.2

## Warning: package 'dplyr' was built under R version 4.2.2

## Warning: package 'stringr' was built under R version 4.2.2

## Warning: package 'forcats' was built under R version 4.2.2

## Warning: package 'lubridate' was built under R version 4.2.2

library(knitr)        # To format tables

## Warning: package 'knitr' was built under R version 4.2.2

library(DAAG)         # To provide collection of function and datasets

## Warning: package 'DAAG' was built under R version 4.2.2

library(ggplot2)      # To visualize data and build visualization
library(psych)        # To produce most frequented requested stats and then read the data frame

## Warning: package 'psych' was built under R version 4.2.2

library(readr)        # To read and parse structured data files
library(dplyr)        # To manipulate and transform data
library(GGally)       # To create complex and multivariate visualizations

## Warning: package 'GGally' was built under R version 4.2.2

#library(qwraps2)     # To make summary tables
#library(naniar)      # To replace missing values
#library(formattable) # To format tables into currency
#library(MASS)        # To calculate VIF

Data Preparation

Data Import

Our data sets include the Listings, and Reviews data sets included in the Airbnb Listings & Reviews. All of the Airbnb data shows <add more here for 2,469(add correct) listings over the span of a 13 years. We will read all of this data into R.

listings <- read.csv("C:/Users/sneha/Downloads/Airbnb+Data/Airbnb Data/Listings.csv")
listings

Read in the data

reviews <- read.csv('C:/Users/sneha/Downloads/Airbnb+Data/Airbnb Data/Reviews.csv')
reviews

encoding the variables for Room type

room_type <- c("Entire place", "Hotel room", "Private room", "Shared room")
room_type_encoded <- factor(room_type, levels = unique(room_type))
as.integer(room_type_encoded)

## [1] 1 2 3 4

#listing_new

Data Cleaning

The first part of data cleaning involves removal of data columns which aren’t required from the data sets.To keep the data not messy, we will simplify each data set to only include the variables we want to analyze.

To focus more on the ‘Price’ segment we added a filter to filter out prices for the listings in the listings data frame.

listing_price <- filter(listings,price>5000 & price<30000)
listing_price

room_type <- c("Entire place", "Hotel room", "Private room", "Shared room")
room_type_encoded <- factor(room_type, levels = unique(room_type))
as.integer(room_type_encoded)

## [1] 1 2 3 4

Listings: host_id ,host_since,host_location, host_total_listings_count, host_has_profile_pic, host_identity_verified ,latitude longitude

listing_new <- listing_price %>%
  subset(select = -c(host_id ,host_since,host_location, host_total_listings_count, host_has_profile_pic, host_identity_verified ,latitude,longitude,district,name))

Reviews: review_id, reviewer_id

reviews_new <- reviews %>%
  subset(select = -c(review_id, reviewer_id))

Removing null values

Here, we have removed the rows with null values for the effective cleaning of the dataset.

# Confirm all missing values are taken care of
listing_new <- na.omit(listing_new)

listing_new

Listing the column names to confirm all missing values are taken care of.

colSums(is.na(listing_new))

##                  listing_id          host_response_time 
##                           0                           0 
##          host_response_rate        host_acceptance_rate 
##                           0                           0 
##           host_is_superhost               neighbourhood 
##                           0                           0 
##                        city               property_type 
##                           0                           0 
##                   room_type                accommodates 
##                           0                           0 
##                    bedrooms                   amenities 
##                           0                           0 
##                       price              minimum_nights 
##                           0                           0 
##              maximum_nights        review_scores_rating 
##                           0                           0 
##      review_scores_accuracy   review_scores_cleanliness 
##                           0                           0 
##       review_scores_checkin review_scores_communication 
##                           0                           0 
##      review_scores_location         review_scores_value 
##                           0                           0 
##            instant_bookable 
##                           0

Key Variables

We will introduce a new variable called Total_Amenities within the transactions data set to help us better understand the price trends.

We also have other existing key variables such as city,room_type, price, amenities.

listing_new <- listing_new %>% mutate(Total_amenities = str_count(amenities, ",") +1)

listing_new

Data Preview

Data Dictionary This dataset includes the following variables:

listing_dict <- read.csv('C:/Users/sneha/Downloads/Airbnb+Data/Airbnb Data/Listings_data_dictionary.csv') 
listing_dict

listing_new

Summary Statistics

The data captured is for the price range from 5000 and abpve. There are 1104 observations in the dataset that range over 9 cities.

The following characteristics that were captured for each sold home are repeated below, and explained in the prior tab:

colnames(listing_new)

##  [1] "listing_id"                  "host_response_time"         
##  [3] "host_response_rate"          "host_acceptance_rate"       
##  [5] "host_is_superhost"           "neighbourhood"              
##  [7] "city"                        "property_type"              
##  [9] "room_type"                   "accommodates"               
## [11] "bedrooms"                    "amenities"                  
## [13] "price"                       "minimum_nights"             
## [15] "maximum_nights"              "review_scores_rating"       
## [17] "review_scores_accuracy"      "review_scores_cleanliness"  
## [19] "review_scores_checkin"       "review_scores_communication"
## [21] "review_scores_location"      "review_scores_value"        
## [23] "instant_bookable"            "Total_amenities"

Below are some summary statistics of the listings sales price, review scores rating:

summary(listing_new$price)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    5001    6143    7880    9037   10000   29500

summary(listing_new$review_scores_rating)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   20.00   95.00   99.00   96.09  100.00  100.00

The average price of listing in Airbnb are $344,774, but this price ranges from $16,000 to $2,700,000.

The average size of homes in Cincinnati is 2,043 square feet, which sit on an average lot size of 11,809 square feet. (This is approximately 0.2711043 acres.)

Data Visualization

The visualization contains spread of the data for the key variables.

This plot shows the relationship between the number of amenities provided by each listing (Total_amenities) and their prices. The ylim() function is used to focus on prices above 5000, while the labs() function adds descriptive labels to the plot.

x1 <- listing_new$Total_amenities
y <- listing_new$price
ggplot(data.frame(x1, y), aes(x = x1, y = y)) + geom_point(color="steelblue") + ylim(5000, max(y)) + labs(x = "Total_amenities", y = "Price", title = "Plot with Price starting from 5000" )

This plot shows the relationship between the type of room (room_type) and their prices. The ylim() function is used to focus on prices above 5000, while the labs() function adds descriptive labels to the plot.

        Note that if room_type is a categorical variable **(e.g., "Entire home/apt", "Private room", "Shared room")**, then the plot will display points at discrete locations on the x-axis for each category. If room_type is a continuous variable (e.g., a numerical score or rating), then the plot will display points at a continuous range of values on the x-axis.

x2 <- listing_new$room_type
y <- listing_new$price
ggplot(data.frame(x2, y), aes(x = x2, y = y)) + geom_point(color="steelblue") + ylim(5000, max(y)) + labs(x = "Room Type", y = "Price", title = "Plot with Price starting from 5000")

This plot shows the relationship between the review score rating (review_scores_rating) and the prices. The ylim() function is used to focus on prices above 5000, while the labs() function adds descriptive labels to the plot.

              Note that if review_scores_rating is a continuous variable (e.g., a numerical score), then the plot will display points at a continuous range of values on the x-axis. If review_scores_rating is a categorical variable (e.g., "Excellent", "Good", "Average", etc.), then the plot will display points at discrete locations on the x-axis for each category.

x3 <- listing_new$review_scores_rating
y <- listing_new$price
ggplot(data.frame(x3, y), aes(x = x3, y = y)) + geom_point(color="steelblue") + ylim(5000, max(y)) + labs(x = "Review Score Rating", y = "Price", title = "Plot with Price starting from 5000")

This plot shows the relationship between the city and the prices. The ylim() function is used to focus on prices above 5000, while the labs() function adds descriptive labels to the plot.

              Note that if city is a categorical variable (e.g., "New York", "Los Angeles", "Chicago", etc.), then the plot will display points at discrete locations on the x-axis for each category. If city is a continuous variable (e.g., a numerical score or index), then the plot will display points at a continuous range of values on the x-axis.

x <- listing_new$city
y <- listing_new$price
ggplot(data.frame(x, y), aes(x = x, y = y)) + geom_point(color="steelblue") + ylim(5000, max(y)) + labs(x = "City", y = "Price", title = "Plot with Price starting from 5000")

This plot shows the relationship between the instant_bookable variable and the prices. The ylim() function is used to focus on prices above 5000, while the labs() function adds descriptive labels to the plot.

               Note that if instant_bookable is a categorical variable (e.g., "True" or "False"), then the plot will display points at discrete locations on the x-axis for each category. If instant_bookable is a continuous variable (e.g., a numerical score or index), then the plot will display points at a continuous range of values on the x-axis.

x <- listing_new$instant_bookable
y <- listing_new$price
ggplot(data.frame(x, y), aes(x = x, y = y)) + geom_point(color="steelblue") + ylim(5000, max(y)) + labs(x = "Instant Bookable", y = "Price", title = "Plot with price starting from 5000")

This plot shows the relationship between the bedrooms variable and the prices. The ylim() function is used to focus on prices above 5000, while the labs() function adds descriptive labels to the plot.

           Note that if bedrooms is a categorical variable (e.g., "1 bedroom", "2 bedrooms", etc.), then the plot will display points at discrete locations on the x-axis for each category. If bedrooms is a continuous variable (e.g., a numerical count), then the plot will display points at a continuous range of values on the x-axis.

x5 <- listing_new$bedrooms
y <- listing_new$price
ggplot(data.frame(x5, y), aes(x = x5, y = y)) + geom_point(color="steelblue") + ylim(5000, max(y)) + labs(x = "Bedrooms", y = "Price", title = "Plot with price starting from 5000")

This plot shows the relationship between the minimum_nights variable and the prices. The xlim() function is used to focus on minimum_nights values between 0 and 25, while the ylim() function is used to focus on prices above 5000. The labs() function adds descriptive labels to the plot.

                Note that if minimum_nights is a categorical variable (e.g., "1 night", "2 nights", etc.), then the plot will display points at discrete locations on the x-axis for each category. If minimum_nights is a continuous variable (e.g., a numerical count), then the plot will display points at a continuous range of values on the x-axis.

x6 <- listing_new$minimum_nights
y <- listing_new$price
ggplot(data.frame(x6, y), aes(x = x6, y = y)) + geom_point(color="steelblue") + xlim(0, 25) + ylim(5000, max(y)) + labs(x = "Minimum Nights", y = "Price", title = "Plot with price starting from 5000")

## Warning: Removed 20 rows containing missing values (`geom_point()`).

This plot shows the relationship between the host_response_rate* variable and the prices. The ylim() function is used to focus on prices above 5000. The labs() function adds descriptive labels to the plot.

                     Note that host_response_rate should be a continuous variable (e.g., a percentage) for this plot to make sense. If host_response_rate is a categorical variable (e.g., "within an hour", "within a day", etc.), then the plot will display points at discrete locations on the x-axis for each category.

x7 <- listing_new$host_response_rate
y <- listing_new$price
ggplot(data.frame(x7, y), aes(x = x7, y = y)) + geom_point(color="steelblue") + ylim(5000, max(y)) + labs(x = "Host Response Rate", y = "Price", title = "Plot with Price starting from 5000")

The same data but by zip code:

plot(listing_new$price , col = "steelblue", lwd = -0.5)

The resulting airbnb_agg data frame will have one row for each unique combination of city and room_type, with columns for the mean price and mean minimum_nights values for each group. The column names will reflect the original variable names used in the cbind() function (i.e., price and minimum_nights).

                          Note that the cbind() function is used to combine the price and minimum_nights variables into a single data frame, which is necessary because aggregate() expects a single data frame as its input. Without using cbind(), we would have to specify each variable separately in the formula passed to aggregate(), which can be tedious and error-prone for larger data frames with many variables.

airbnb_agg <- aggregate(cbind(price, minimum_nights) ~ city + room_type, data = listing_new, FUN = mean)
airbnb_agg

The resulting plot will show the mean price values for each unique combination of city and room_type, with different colors used to distinguish between the different room_type values. The x axis will display the city values, and the y axis will display the mean price values. The main title will be “Price as per Room Type”, and the subtitle will be “Price upto 50000”.

ggplot(airbnb_agg, aes(x = city, y = price, color = room_type)) +
  geom_point() +
 labs(title = "Price as per Room Type",
        subtitle = "Price upto 50000",
        x = "city",
        y = "price", 
        color = "room type")

listings_fit2 <- listing_new[c(3,11,13,14,16,24)]
listings_fit2

pairs(listings_fit2,col="steelblue" ,pch = 18,                                            
      labels = c("host_response_rate", "bedrooms", "price","minimum_nights","review_scores_rating","Total_amenities"),                  
      main = "This is a pairs plot in R")

The “city” column will contain the unique values of the “city” variable in the listings_new data set, and the “price” column will contain the mean price of listings for each city.

average_price_by_city <- aggregate(price ~ city, data = listing_new, FUN = mean)
average_price_by_city

barplot(average_price_by_city$price, names.arg = average_price_by_city$city,las=2 , ylab = "Average Price", main = "Average Price by City", col = "steelblue")

review_rating_by_city <- aggregate(price ~ Total_amenities, data = listing_new, FUN = mean)
review_rating_by_city

avg_price_by_room_type <- aggregate(price ~ room_type, data = listing_new, FUN = mean)
barplot(avg_price_by_room_type$price, names.arg = avg_price_by_room_type$room_type, xlab = "Room Type", ylab = "Average Price", main = "Average Price by Room Type")

plot(listing_new$minimum_nights, listing_new$price, xlab = "Minimum Nights", ylab = "Price", main = "Price vs. Minimum Nights", col = "steelblue")

Modeling

The process of determining an appropriate model to represent home values in the Cincinnati is two-fold. First, we need to perform a residual analysis. Through this analysis, we can ensure that the full model - that is all the possible covariates along with the response variable - meets the following criteria for linear regression:

The relationship between the regressors and the response variable is approximately linear
Errors are independent
Errors are normally distributed
Error term has an equal/constant variance

If all of these assumptions are not met, variables in the model must be transformed and checked in a process called Model Adequacy Checking, which involves Transformation and Residual Analysis.

Residual Analysis

Let’s begin with a full model. We can create a dataset on which to fit a model, shown below. Note that we are removing amenities, accomodates, neighbourhood, city and multiple review scores from this dataset, as they are not covariates we want to include in our model. Amenities and neighbourhood are not generalizable.

listings_fit <- listing_new[c(3,9,11,13,14, 16,24)]

The residuals function returns the residuals (i.e., the difference between the observed values and the predicted values) from the linear regression model.

In this case, the residuals are the difference between the actual price of each Airbnb listing and the predicted price based on the values of the predictors in the model.

listings_model <- lm(price ~ ., data = listings_fit)

Each point on the plot represents the difference between the actual value and the predicted value of the dependent variable price for a particular observation in the dataset. The pch=20 argument specifies the shape of the points on the plot to be circles. The abline function adds a horizontal line at y=0 to make it easier to see the distribution of the residuals around zero.

plot(listings_model$fitted.values,listings_model$residuals,pch=20)
abline(h=0,col="grey")

In this case, the residuals appear to be fairly normally distributed, except for some deviations from the line in the tails. This suggests that the model is a reasonable fit to the data, but there may be some outliers or heavy-tailed distributions that are not captured by the model.

qqnorm(listings_model$residuals,main="listings_model")
qqline(listings_model$residuals)

Variable Selection

We have satisfied the linear regression assumptions by transforming the variables accordingly. Now we can move into the phase of selecting the variables from this full model to determine the optimal combination/selection of regressors to best model their relationship with Final listing Price.

Forward Selection + Backward Elimination

When attempting to use the step function, I keep getting a message that says “attempting model selection on an essentially perfect fit is nonsense”, but when tested, we get a predicted R squared of above around 50%. Our hypothesis is that this is due to varying levels of certain amenities. Therefore we would be more beneficial to manually select variables through forward selection and backward elimination.

drop1(lm(price ~ x1 + x2 + x3 + x5 + x6 + x7,data=listings_fit), test="F")

We found the best model to be:

drop1(lm(price ~ x3 + x5 + x6 + x7,data=listings_fit), test="F")

drop1(lm(price ~ x5 + x7,data=listings_fit), test="F")

Model Validation

The Final Model to be Validated:

finalmodel = lm(price ~ bedrooms + host_response_rate, data=listings_fit)

summary(finalmodel)

## 
## Call:
## lm(formula = price ~ bedrooms + host_response_rate, data = listings_fit)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##  -8671  -2589  -1174   1199  20605 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          7708.1      680.4  11.329   <2e-16 ***
## bedrooms              635.7       70.1   9.068   <2e-16 ***
## host_response_rate  -1355.6      675.1  -2.008   0.0449 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4074 on 1065 degrees of freedom
## Multiple R-squared:  0.0731, Adjusted R-squared:  0.07136 
## F-statistic:    42 on 2 and 1065 DF,  p-value: < 2.2e-16

finalmodel1 = lm(price ~ . , data=listings_fit)

summary(finalmodel1)$r.squared

## [1] 0.07671024

Here we performed K-fold validation to cross verify the model which is created.

KCV=cv.lm(data=listings_fit, finalmodel1, m=3, seed=123)

## Warning in cv.lm(data = listings_fit, finalmodel1, m = 3, seed = 123): 
## 
##  As there is >1 explanatory variable, cross-validation
##  predicted values for a fold are not a linear function
##  of corresponding overall predicted values.  Lines that
##  are shown for the different folds are approximate

## 
## fold 1 
## Observations in test set: 356 
##                   114      118       128       138       139       140
## Predicted    8954.794 7506.005  8498.680  7366.870  8438.880  9031.452
## cvpred       9172.750 7504.400  8915.677  7288.207  8489.888  8954.982
## price        7153.000 9441.000  5244.000 12000.000  5162.000  6300.000
## CV residual -2019.750 1936.600 -3671.677  4711.793 -3327.888 -2654.982
##                   143       147       179       185       187      188
## Predicted   10383.114  9051.819  8761.474 9173.5025 8790.5846 8769.483
## cvpred      10399.048  9102.600  8705.297 9305.4084 8893.2909 8833.620
## price       14455.000  5750.000 12390.000 8559.0000 9550.0000 8247.000
## CV residual  4055.952 -3352.600  3684.703 -746.4084  656.7091 -586.620
##                   193       194       200       213       215      216
## Predicted    8503.174 8269.8992  9477.392 8594.6090 8645.9148 8609.366
## cvpred       8645.404 8349.8788  9329.587 8545.2145 8619.5513 8563.363
## price        6999.000 8655.0000  8000.000 8000.0000 9500.0000 9808.000
## CV residual -1646.404  305.1212 -1329.587 -545.2145  880.4487 1244.637
##                   217       218       221       222       295       297
## Predicted    7618.226  7632.983  7826.585  8422.681  8845.839  8882.988
## cvpred       7651.144  7669.293  8025.260  8219.345  8982.555  8983.879
## price        5080.000  5906.000  5895.000  6300.000  6143.000  6132.000
## CV residual -2571.144 -1763.293 -2130.260 -1919.345 -2839.555 -2851.879
##                   312       314       331       333       334       335
## Predicted    8818.394  8126.874  8250.677 8398.0180  8331.677  8321.704
## cvpred       8881.361  8128.454  8370.030 8365.8562  8547.128  8547.302
## price       10000.000  6377.000  6195.000 9000.0000  6491.000  5571.000
## CV residual  1118.639 -1751.454 -2175.030  634.1438 -2056.128 -2976.302
##                   337       360       361      362      373       380       394
## Predicted    7542.419 7958.7980  7562.186 7816.779 6743.727  7000.722  8933.003
## cvpred       7697.101 8453.9142  7630.290 8303.078 6673.916  7127.250  9134.711
## price        5043.000 8175.0000  6121.000 9800.000 8614.000 10219.000  5264.000
## CV residual -2654.101 -278.9142 -1509.290 1496.922 1940.084  3091.750 -3870.711
##                   396       399       402       403       405       411
## Predicted    9552.027  9628.618  8875.112  8269.018 12768.875 9459.8087
## cvpred       9720.379  9927.573  8833.920  8516.228 12955.191 9450.2051
## price        6204.000  8253.000  5995.000  5110.000 21830.000 9262.0000
## CV residual -3516.379 -1674.573 -2838.920 -3406.228  8874.809 -188.2051
##                   417        418       419       433       434      435
## Predicted   10170.270 8744.05149  7729.805  8461.321 14283.940  8198.17
## cvpred      10294.447 9048.45783  7595.173  8544.869 14168.271  8405.42
## price       11968.000 9026.00000  5200.000 12000.000  5309.000  6000.00
## CV residual  1673.553  -22.45783 -2395.173  3455.131 -8859.271 -2405.42
##                  439       443       444       452       495       499
## Predicted    9528.99  8881.832  9564.159 9489.7267  9554.186 8249.3865
## cvpred       9589.09  8923.861  9688.541 9449.6839  9688.715 8446.5255
## price       12500.00  5007.000 16000.000 9000.0000 19308.000 8000.0000
## CV residual  2910.91 -3916.861  6311.459 -449.6839  9619.285 -446.5255
##                   503       504       511       514       521       526
## Predicted   8097.5387  9388.405  9849.927  8892.960 11006.496 8905.8721
## cvpred      8158.6198  9597.237  9831.846  8983.705 11366.646 8963.4675
## price       7500.0000  8000.000  6131.000 10429.000  8000.000 8001.0000
## CV residual -658.6198 -1597.237 -3700.846  1445.295 -3366.646 -962.4675
##                    536       538       540       551       555       565
## Predicted    9307.1186 8839.6297  9609.300 8427.5233 8312.0449 9033.6348
## cvpred       9404.9528 8804.5187  9787.819 8775.6058 8477.4248 9381.5116
## price       10000.0000 8500.0000 12420.000 9500.0000 8000.0000 9995.0000
## CV residual   595.0472 -304.5187  2632.181  724.3942 -477.4248  613.4884
##                   567       568         575       576       581       583
## Predicted    8718.632  9476.815  9687.82656  8959.848 8969.1756  9597.858
## cvpred       8679.392  9469.922 10066.63122  9290.768 9142.4803  9798.025
## price        7257.000 16429.000 10000.00000 10506.000 9714.0000  5286.000
## CV residual -1422.392  6959.078   -66.63122  1215.232  571.5197 -4512.025
##                  584       590       592       593       597       600
## Predicted    9502.97  8972.394  9672.379  9590.824  9483.849  8833.331
## cvpred       9647.61  8972.621 10070.114  9778.135  9489.812  8965.973
## price        7457.00 15054.000 11760.000  6561.000  6286.000  5575.000
## CV residual -2190.61  6081.379  1689.886 -3217.135 -3203.812 -3390.973
##                   603       612       613       617       626       633
## Predicted    8957.733  9708.238 9036.5738 9595.6983 8964.7671  9554.365
## cvpred       9152.686 10147.934 9361.4476 9829.6889 9172.5764  9755.178
## price        8045.000  9787.000 9025.0000 9077.0000 9018.0000  8708.000
## CV residual -1107.686  -360.934 -336.4476 -752.6889 -154.5764 -1047.178
##                   692       693       694       695       696       698
## Predicted    9036.574  8230.579  8868.410 10665.849 10215.501  8833.931
## cvpred       9361.448  8218.677  9032.193 10771.466 10426.957  8911.110
## price        8003.000  5885.000  6700.000  5148.000  5817.000  5500.000
## CV residual -1358.448 -2333.677 -2332.193 -5623.466 -4609.957 -3411.110
##                   699       706       708       713       717      719
## Predicted    8825.517  8686.492 8926.9733  8939.526 8214.9078 8846.663
## cvpred       8934.483  8593.108 9023.1384  9242.696 8325.4421 8824.409
## price        7000.000  5800.000 8786.0000  5790.000 7400.0000 9000.000
## CV residual -1934.483 -2793.108 -237.1384 -3452.696 -925.4421  175.591
##                   722       726       731       735       739       745
## Predicted    8371.254  8926.973  9640.060  8983.243 8293.8827 8565.2587
## cvpred       8616.483  9023.138  9917.367  9182.261 8397.6898 9193.4762
## price        7607.000 28571.000 10141.000 19520.000 8060.0000 8900.0000
## CV residual -1009.483 19547.862   223.633 10337.739 -337.6898 -293.4762
##                   747      778       779       780       782      785       789
## Predicted    8762.124 8265.434  8194.407  8314.670  8399.075  7814.53  7532.492
## cvpred       8722.239 8388.179  8210.908  8527.411  8766.095  8301.51  7527.530
## price       12800.000 8446.000  7000.000  6142.000 10058.000  5386.00  5529.000
## CV residual  4077.761   57.821 -1210.908 -2385.411  1291.905 -2915.51 -1998.530
##                    790       793       794       795       796       797
## Predicted   8919.62587  8181.030  8974.516  8987.893 10115.470  8145.861
## cvpred      9073.29859  8149.495  9275.685  9337.097 10125.293  8050.044
## price       9000.00000 12500.000  6000.000  7846.000  8714.000  6500.000
## CV residual  -73.29859  4350.505 -3275.685 -1491.097 -1411.293 -1550.044
##                   798       799       804        887       890       894
## Predicted    9552.716  9011.064 10759.868  9674.9371  9548.207  8089.238
## cvpred       9698.747  9331.873 10877.049  9553.3977  9617.090  8114.423
## price        5900.000  6500.000 12000.000 10000.0000  5057.000  5219.000
## CV residual -3798.747 -2831.873  1122.951   446.6023 -4560.090 -2895.423
##                   902       913      915       919       921       924
## Predicted    8827.700 11004.938 11694.74  9663.853  9185.236  8502.909
## cvpred       8802.018 11311.589 11747.36  9602.062  9583.798  8819.118
## price        7199.000  6743.000 23705.00 13268.000  7429.000  7000.000
## CV residual -1603.018 -4568.589 11957.64  3665.938 -2154.798 -1819.118
##                   929       931        933       934       936       938
## Predicted   10321.069 10065.056 9218.44179  8546.840 9823.8236  9229.167
## cvpred      10585.936  9994.986 9439.02462  8513.163 9847.2915  9277.843
## price        5900.000  6500.000 9429.00000  6600.000 9950.0000  7900.000
## CV residual -4685.936 -3494.986  -10.02462 -1913.163  102.7085 -1377.843
##                   942       945       950       951       952      955     1078
## Predicted   7771.2571  9209.209  9858.992  8463.556  9147.701  9253.52 11698.92
## cvpred      7881.9729  9231.527  9946.743  8646.480  9019.096  9247.40 11824.66
## price       7057.0000  6500.000  7500.000 12000.000  6900.000  6500.00  5900.00
## CV residual -824.9729 -2731.527 -2446.743  3353.520 -2119.096 -2747.40 -5924.66
##                  1080      1089      1090      1099     1104      1108
## Predicted   14634.588  9248.046 10905.195  9050.126 8704.233  8942.286
## cvpred      14505.529  9508.554 10971.615  9215.914 8794.170  9156.169
## price        6500.000  7500.000 14500.000  6622.000 8000.000  6730.000
## CV residual -8005.529 -2008.554  3528.385 -2593.914 -794.170 -2426.169
##                  1110      1115      1117      1126      1127      1130
## Predicted    8261.339  9092.844 10580.323 8195.0970  9005.545  9565.404
## cvpred       8348.225  9520.570 11297.953 8189.2758  9504.927  9781.792
## price       12500.000  6000.000  7345.000 7714.0000  6879.000  7113.000
## CV residual  4151.775 -3520.570 -3952.953 -475.2758 -2625.927 -2668.792
##                  1132      1138      1144      1145      1152      1159
## Predicted    9650.499  8891.491  8322.573  8575.231  9483.849 8377.2836
## cvpred       9998.843  8993.737  8592.133  9193.302  9489.812 8728.0559
## price        5347.000 23300.000  5342.000  5500.000 15000.000 9000.0000
## CV residual -4651.843 14306.263 -3250.133 -3693.302  5510.188  271.9441
##                   1175      1176      1180      1184      1187      1280
## Predicted   9018.41161  8915.621  8898.838  8237.747  8884.771 8412.2794
## cvpred      9281.71254  9066.576  8943.577  8474.776  8903.797 8057.2375
## price       9300.00000  5999.000  7143.000  5500.000 12000.000 7447.0000
## CV residual   18.28746 -3067.576 -1800.577 -2974.776  3096.203 -610.2375
##                  1300      1307      1314      1319      1321      1323
## Predicted   12925.867 8805.7905  9668.369  9597.277 11804.747  8352.262
## cvpred      13072.785 8962.7202  9789.983  9683.026 11519.867  8421.485
## price       11750.000 8529.0000  5147.000  6200.000 16347.000  5200.000
## CV residual -1322.785 -433.7202 -4642.983 -3483.026  4827.133 -3221.485
##                 1329      1331      1378      1379      1380      1382
## Predicted   10448.03  7915.735  8147.975 11994.375  8261.895 11241.711
## cvpred      10603.25  8031.138  8188.125 12123.313  8463.107 11159.729
## price       28098.00 21433.000  5183.000  6143.000  6000.000 20000.000
## CV residual 17494.75 13401.862 -3005.125 -5980.313 -2463.107  8840.271
##                  1384      1387     1402       1407      1409       1418
## Predicted   10224.880  8851.403 13300.55 7518.33460  9631.922 9356.50702
## cvpred       9952.665  9012.477 13322.24 7454.51732  9511.453 9323.16347
## price        5500.000  5504.000 27563.00 7500.00000 20500.000 9300.00000
## CV residual -4452.665 -3508.477 14240.76   45.48268 10988.547  -23.16347
##                  1425      1426      1432      1437      1438      1442
## Predicted   10099.933  9565.314  8297.063 10830.116  8858.437  8902.709
## cvpred      10095.544  9748.560  8562.558 11042.721  9032.367  9086.814
## price        6000.000  5200.000  5999.000  7016.000  5055.000 13549.000
## CV residual -4095.544 -4548.560 -2563.558 -4026.721 -3977.367  4462.186
##                  1444      1445      1448      1453      1455      1456
## Predicted    8964.633 7816.9204  8319.544  6906.595  9649.719 12597.127
## cvpred       9309.090 7637.5827  8578.965  6775.693  9987.244 12497.887
## price        6929.000 8000.0000  5999.000  5204.000 14571.000  6000.000
## CV residual -2380.090  362.4173 -2579.965 -1571.693  4583.756 -6497.887
##                  1457      1458     1460     1465     1758      1761      1823
## Predicted   12737.801  8925.190 10683.79 13982.88 6928.916  6951.486  7062.674
## cvpred      12895.693  9103.221 10581.76 14086.92 6938.379  6988.017  6849.827
## price       18000.000  8000.000  7227.00 22000.00 8000.000 20000.000 10000.000
## CV residual  5104.307 -1103.221 -3354.76  7913.08 1061.621 13011.983  3150.173
##                  1837      1897      1905     1910      1914      1917
## Predicted    7468.641 6864.1429 6899.3114 7103.009 6176.4118  7001.912
## cvpred       6992.021 6769.3977 6868.8493 6901.500 5828.5163  6945.771
## price       11644.000 5800.0000 5990.0000 9999.000 5679.0000  5202.000
## CV residual  4651.979 -969.3977 -878.8493 3097.500 -149.5163 -1743.771
##                  1922       2149      2181       2208     2216      2217
## Predicted    7332.228 6920.41259  6975.510  9724.0881 6337.345  7148.619
## cvpred       7408.199 6928.52027  6697.671  9616.5612 6155.925  7237.958
## price        5202.000 6900.00000 10000.000 10000.0000 8260.000 10491.000
## CV residual -2206.199  -28.52027  3302.329   383.4388 2104.075  3253.042
##                  2297      2304      2306      2308      2310      2313
## Predicted    8230.266 10235.043 10142.225  8209.164 11833.469 10452.917
## cvpred       8288.727 10463.428 10248.118  8229.056 11710.667 10931.008
## price        6500.000  6500.000  5162.000  6000.000  6666.000  6643.000
## CV residual -1788.727 -3963.428 -5086.118 -2229.056 -5044.667 -4288.008
##                  2316      2323      2326      2334      2348      2349
## Predicted    9053.580  9614.864  8887.396  8344.274 7964.1597  8907.028
## cvpred       9381.164  9817.742  8953.783  8596.940 7715.4164  9023.486
## price        8000.000 13143.000  5500.000  6105.000 7500.0000  7571.000
## CV residual -1381.164  3325.258 -3453.783 -2491.940 -215.4164 -1452.486
##                 2369      2373      2374      2376      2379     2385      2387
## Predicted   8085.216 8227.4162  9670.540  9030.416  8260.515 11348.60 8172.5263
## cvpred      7679.520 8342.0231  9502.746  8857.407  8506.370 11414.82 8139.6369
## price       9998.000 8500.0000  8013.000  5845.000  6500.000 14143.00 8500.0000
## CV residual 2318.480  157.9769 -1489.746 -3012.407 -2006.370  2728.18  360.3631
##                  2398      2404      2410      2427      2438      2439
## Predicted   8007.5207  9633.302  9563.469  8265.327  8997.776 10812.778
## cvpred      8152.9895  9468.190  9710.173  8439.455  9303.692 11177.563
## price       7900.0000  8013.000  8118.000  6500.000  5157.000  9840.000
## CV residual -252.9895 -1455.190 -1592.173 -1939.455 -4146.692 -1337.563
##                  2444      2447      2461      2463      2465      2466
## Predicted    9557.080  8248.007  9482.379  8193.187  9480.910  9794.846
## cvpred       9838.396  8489.789  9499.844  8107.893  9509.876  9491.245
## price        5500.000 11051.000 12000.000  5747.000  7500.000 25200.000
## CV residual -4338.396  2561.211  2500.156 -2360.893 -2009.876 15708.755
##                  2509        2510      2512      2514      2516      2518
## Predicted    8250.766  9753.22690  7548.118  9602.580  9720.056  8945.449
## cvpred       8403.262 10095.51107  7590.510  9697.878 10186.147  9032.823
## price        6000.000 10000.00000  5001.000 11250.000  6283.000  6000.000
## CV residual -2403.262   -95.51107 -2589.510  1552.122 -3903.147 -3032.823
##                  2520      2532      2542      2545      2550       2551
## Predicted    8365.376  8379.443  8181.854  8221.762  9341.369 10377.9664
## cvpred       8656.611  8696.392  8364.072  8278.869  9722.549 10862.8022
## price        6743.000  7517.000  6000.000 10000.000  7240.000  9886.0000
## CV residual -1913.611 -1179.392 -2364.072  1721.131 -2482.549  -976.8022
##                   2553     2555      2559      2560       2562      2577
## Predicted   10180.2428 10371.62 10160.611 10271.681 10146.5437  8941.320
## cvpred      10294.2735 10821.28 10224.571 10552.848 10184.7899  8913.124
## price       10142.0000 11993.00 18000.000 18000.000 10029.0000  5500.000
## CV residual  -152.2735  1171.72  7775.429  7447.152  -155.7899 -3413.124
##                  2623     2630      2633      2635      2636      2639
## Predicted    8862.935 8981.774 8926.9733 8907.0279  8233.518  9735.683
## cvpred       9035.503 9192.293 9023.1384 9023.4859  8198.613 10249.127
## price       15357.000 8500.000 8140.0000 8713.0000  6500.000 12286.000
## CV residual  6321.497 -692.293 -883.1384 -310.4859 -1698.613  2036.873
##                  2643       2646      2647      2652      2653     2654
## Predicted    8231.735 8460.06663  8876.044 9032.4790  8441.591 8845.194
## cvpred       8278.695 8825.07098  8997.220 9321.4932  8815.386 8834.441
## price        5679.000 8888.00000  5466.000 9429.0000 10000.000 8000.000
## CV residual -2599.695   62.92902 -3531.220  107.5068  1184.614 -834.441
##                  2660      2785      2786      2790      2791      2794
## Predicted    8966.550 7373.3150  9586.954  8956.197  8394.930  7957.208
## cvpred       9092.494 7370.2486  9603.040  9143.562  8654.335  7920.983
## price        6600.000 6888.0000  8160.000  6263.000  5162.000 19500.000
## CV residual -2492.494 -482.2486 -1443.040 -2880.562 -3492.335 11579.017
##                  2795      2802      2803     2804      2811      2813
## Predicted    7969.267 10288.912 9136.7401 7742.483  8495.495  8973.540
## cvpred       8207.844 10437.424 9494.7399 7895.849  8477.400  9250.272
## price        6143.000  9000.000 8550.0000 8000.000  6650.000  8000.000
## CV residual -2064.844 -1437.424 -944.7399  104.151 -1827.400 -1250.272
##                  2816      2824      2825      2827      2828      2830
## Predicted   11117.826  8981.051 8847.5052  7820.218 10863.637  9396.871
## cvpred      11247.801  8882.786 8779.6529  8084.540 11000.387  9735.140
## price        6857.000  6156.000 8200.0000  5171.000  5575.000  8285.000
## CV residual -4390.801 -2726.786 -579.6529 -2913.540 -5425.387 -1450.140
##                  2831      2832      2834       2835      2838      2842
## Predicted    8845.643  9822.735  9165.402  9839.3605  9467.203  9072.921
## cvpred       8968.741 10179.151  9548.434  9877.0401  9402.790  9162.271
## price       11000.000 11026.000 18000.000 10450.0000 11000.000  5990.000
## CV residual  2031.259   846.849  8451.566   572.9599  1597.210 -3172.271
##                 2879      2881      2882      2886      2887      2891
## Predicted   10386.47 9019.1416 8487.8760 8855.2257 10571.399  9952.094
## cvpred      10551.10 9189.6489 8536.2918 8708.8508 10337.738  9818.477
## price        7134.00 8950.0000 7938.0000 9000.0000  7282.000  5700.000
## CV residual -3417.10 -239.6489 -598.2918  291.1492 -3055.738 -4118.477
##                   2892      2893       2913      2928      2961      2964
## Predicted    9848.6721 10604.704  9530.5238 10979.161  8866.295 9067.6476
## cvpred      10007.3895 10581.199  9612.1726 11128.822  8894.112 9420.9448
## price       10600.0000  7000.000 10000.0000 17500.000  5137.000 9143.0000
## CV residual   592.6105 -3581.199   387.8274  6371.178 -3757.112 -277.9448
##                  2966      2969      2973      2980      2994      2995
## Predicted    8380.913  9022.506 9588.7542 10227.409  8871.304 10149.438
## cvpred       8686.360  9321.667 9843.0302 10498.401  9181.875 10334.471
## price        6459.000  5335.000 9000.0000  7523.000  5950.000  7890.000
## CV residual -2227.360 -3986.667 -843.0302 -2975.401 -3231.875 -2444.471
##                  2996      2999      3003      3006      3011       3201
## Predicted    9609.300  7723.782  8319.392  8331.766 10235.357 10344.3523
## cvpred       9787.819  8021.304  8427.265  8580.359 10393.378 10513.1414
## price       12500.000 10357.000 15000.000  5500.000  7000.000 11102.0000
## CV residual  2712.181  2335.696  6572.735 -3080.359 -3393.378   588.8586
##                  3202      3203      3204      3208      3212      3217
## Predicted   10063.272 11469.993 10196.779  9778.284  9077.481 8753.4978
## cvpred      10189.946 11602.441 10331.653 10058.241  9283.876 8669.5712
## price       12066.000 15923.000 13950.000  5767.000  7950.000 8888.0000
## CV residual  1876.054  4320.559  3618.347 -4291.241 -1333.876  218.4288
##                  3220      3237      3291      3295      3305      3306
## Predicted    8395.598  8380.841 13365.417 10131.007  8342.805  8284.000
## cvpred       8411.944  8393.796 13524.451 10155.041  8606.972  8431.095
## price        6500.000  6500.000  8600.000  8648.000  5571.000  6174.000
## CV residual -1911.944 -1893.796 -4924.451 -1507.041 -3035.972 -2257.095
##                  3309      3310     3313      3315      3325      3327
## Predicted    8313.980  8277.432 8210.634 8242.8635  7231.690  7568.350
## cvpred       8549.043  8492.855 8219.024 8338.5401  7101.399  7605.349
## price        5343.000  6428.000 9520.000 7647.0000  5850.000  6286.000
## CV residual -3206.043 -2064.855 1300.976 -691.5401 -1251.399 -1319.349
##                  3328      3339     3340      3341     3342      3343      3364
## Predicted    7794.899  6957.051 7126.174  6958.520 7541.729  7312.645 7010.4710
## cvpred       8231.807  7017.940 7425.257  7007.908 7718.733  7448.242 7230.3581
## price       11559.000  5071.000 9272.000  5403.000 6900.000 10000.000 7406.0000
## CV residual  3327.193 -1946.940 1846.743 -1604.908 -818.733  2551.758  175.6419
##                  3373      3374      3376      3378      3442      3443
## Predicted   10778.165 8918.1564  8237.299  8868.920  8356.272 10276.555
## cvpred      10820.271 9083.3306  8308.618  8944.098  8701.617 10604.402
## price       13502.000 8759.0000  5478.000 13489.000  6625.000  6132.000
## CV residual  2681.729 -324.3306 -2830.618  4544.902 -2076.617 -4472.402
##                  3447       3454
## Predicted    8328.738 7641.49176
## cvpred       8567.192 7920.70217
## price        6107.000 8000.00000
## CV residual -2460.192   79.29783
## 
## Sum of squares = 5332029630    Mean square = 14977611    n = 356 
## 
## fold 2 
## Observations in test set: 356 
##                   110       111       113       127       144        160
## Predicted   9380.4575  8156.568  7503.577  9201.079  8490.876  9733.5411
## cvpred      9463.0658  8373.965  7754.378  9507.559  8684.496  9811.6189
## price       9000.0000  5071.000  5500.000  6500.000  5162.000 10014.0000
## CV residual -463.0658 -3302.965 -2254.378 -3007.559 -3522.496   202.3811
##                   165       166       167      170       180       181
## Predicted    9074.011  9618.111  7868.058  9621.18 8424.7589  9729.912
## cvpred       9282.574 10068.803  8149.410  9628.00 8565.8169  9805.434
## price       10800.000  6500.000  5162.000 13591.00 7847.0000 12424.000
## CV residual  1517.426 -3568.803 -2987.410  3963.00 -718.8169  2618.566
##                   190       195       204       208       219       294
## Predicted    8760.004 8129.3591  8127.604  7770.315  7689.253  8592.759
## cvpred       8957.506 8534.7176  8388.233  7990.097  7880.891  8881.008
## price        7227.000 8959.0000 11357.000  6895.000  5500.000 11599.000
## CV residual -1730.506  424.2824  2968.767 -1095.097 -2380.891  2717.992
##                   296      305       307       311       322       323      324
## Predicted    8817.704 8622.875  8846.439  8885.927 8150.9144  8165.493 8084.762
## cvpred       8934.733 8861.328  8926.227  8944.501 8359.2555  8326.619 8332.726
## price        5885.000 9280.000  6000.000 16286.000 9301.0000  6429.000 9800.000
## CV residual -3049.733  418.672 -2926.227  7341.499  941.7445 -1897.619 1467.274
##                   327       330       332      336       358       359
## Predicted    8307.636  8338.710 8314.6701 7615.651  7529.777  7646.411
## cvpred       8403.211  8429.125 8406.7466 7825.365  7777.055  7825.383
## price        5457.000  5776.000 8000.0000 8000.000  6300.000  5162.000
## CV residual -2946.211 -2653.125 -406.7466  174.635 -1477.055 -2663.383
##                   365       372       381       390       391       392
## Predicted   7562.0064  6947.257  6956.450  7682.359 8181.0295  8171.236
## cvpred      7782.9595  7252.227  7256.062  7854.533 8339.5753  8358.388
## price       6880.0000 10220.000 10219.000  5162.000 8000.0000  5851.000
## CV residual -902.9595  2967.773  2962.938 -2692.533 -339.5753 -2507.388
##                   393       397       401       404       408       409
## Predicted   8209.1644  9452.775  9568.253 11469.640  8140.252  8727.000
## cvpred      8353.7166  9464.598  9532.935 11249.579  8349.535  8925.532
## price       8000.0000  6768.000  7562.000  6657.000  7000.000  7373.000
## CV residual -353.7166 -2696.598 -1970.935 -4592.579 -1349.535 -1552.532
##                   414       415       420       441       448       449
## Predicted    8609.631  8661.627  8251.501  8338.710 11410.100  7920.610
## cvpred       8908.076  8910.475  8434.335  8429.125 11215.721  8184.545
## price        7260.000  7728.000  6808.000  5938.000 10000.000  6000.000
## CV residual -1648.076 -1182.475 -1626.335 -2491.125 -1215.721 -2184.545
##                   454       502       519       527       528       530
## Predicted    8378.287  8240.417  9121.292  8310.575  9517.862  8255.775
## cvpred       8464.460  8481.382  9098.834  8414.983  9528.197  8392.587
## price        7213.000  5988.000  6999.000  5514.000  5030.000  6000.000
## CV residual -1251.460 -2493.382 -2099.834 -2900.983 -4498.197 -2392.587
##                   531       534       537       554       560       564
## Predicted    9049.799 8913.3717  9581.165 7801.9323  8365.376 8836.6908
## cvpred       9083.490 8964.2296  9560.015 7914.6338  8437.380 8919.7539
## price        8000.000 9214.0000  6000.000 7071.0000  6833.000 8500.0000
## CV residual -1083.490  249.7704 -3560.015 -843.6338 -1604.380 -419.7539
##                   577      578      579       585        587        589
## Predicted   8919.9396 8226.171 10153.58  9900.632  9461.5469 10120.6130
## cvpred      8982.1868 8372.559 10077.76 10069.301  9525.1997 10102.7285
## price       8000.0000 9544.000 17671.00  5981.000 10070.0000  9195.0000
## CV residual -982.1868 1171.441  7593.24 -4088.301   544.8003  -907.7285
##                   594       595       596       601         614        629
## Predicted   10208.467 10299.816  9643.554  9772.231 12041.67583 10201.3440
## cvpred      10117.217 10146.116  9588.585  9635.460 11798.80689 10096.6215
## price        7392.000 11172.000 11471.000 18857.000 11733.00000 11060.0000
## CV residual -2725.217  1025.884  1882.415  9221.540   -65.80689   963.3785
##                   636       689       690       691       697       700
## Predicted    9591.165  8934.600  8186.863  9873.259  9434.147  8299.312
## cvpred       9649.760  9472.389  8388.405 10166.356  9547.817  8427.910
## price        8280.000  8000.000  6367.000  8060.000  8389.000  5814.000
## CV residual -1369.760 -1472.389 -2021.405 -2106.356 -1158.817 -2613.910
##                  701       702       705       709       711       715
## Predicted   8935.342  8213.573  9672.603 8307.9501  8216.288  8831.127
## cvpred      9003.369  8371.375  9605.974 8429.1063  8374.312  8922.105
## price       9984.000  5157.000 11232.000 8736.0000  6250.000  7177.000
## CV residual  980.631 -3214.375  1626.026  306.8937 -2124.312 -1745.105
##                   716       720       721       724       727       734
## Predicted    9623.367  9060.614  9424.819  8959.203  9582.410  8338.710
## cvpred       9581.227  9052.893  9484.577  8991.627  9557.066  8429.125
## price       12400.000 29500.000  8071.000 11000.000  5995.000  7000.000
## CV residual  2818.773 20447.107 -1413.577  2008.373 -3562.066 -1429.125
##                   736       738       740       744       749       769
## Predicted    8976.209  8987.651  9524.895  8870.704  8482.558  8149.445
## cvpred       9010.469  9031.663  9531.732  8957.440  8926.494  8353.369
## price       18720.000 15000.000 24800.000 12480.000  5872.000  5500.000
## CV residual  9709.531  5968.337 15268.268  3522.560 -3054.494 -2853.369
##                   772        774       787       788       792       802
## Predicted    8160.063 11457.6421 8228.8857  8172.616  7639.377 10762.628
## cvpred       8388.375 11225.7472 8375.4968  8347.214  7821.848 10619.069
## price        6843.000 10857.0000 9000.0000  7186.000  6583.000  7908.000
## CV residual -1545.375  -368.7472  624.5032 -1161.214 -1238.848 -2711.069
##                   803       805        808       817      818       891
## Predicted   8722.8161  8136.202  9990.3772  7538.145 7590.141  6742.485
## cvpred      8916.7087  8400.118 10032.9075  7794.702 7797.101  8117.018
## price       8050.0000  5500.000 10500.0000 10000.000 9999.000  5265.000
## CV residual -866.7087 -2900.118   467.0925  2205.298 2201.899 -2852.018
##                   892       893       896       898       905       906
## Predicted    8749.324  8050.619  8948.204 8955.9278 11314.143  9891.156
## cvpred       9087.174  8410.178  9109.996 9107.9442 11323.089 10046.869
## price        6500.000  6300.000 13500.000 9507.0000  8359.000 18000.000
## CV residual -2587.174 -2110.178  4390.004  399.0558 -2964.089  7953.131
##                   908       909       911       914       918       923
## Predicted    9500.233  9625.950  9084.038  9016.752 10273.992  8406.182
## cvpred       9564.477  9841.503  9087.831  9088.500 10213.466  8581.188
## price        8099.000 11500.000  6000.000 17493.000  5325.000  5835.000
## CV residual -1465.477  1658.497 -3087.831  8404.500 -4888.466 -2746.188
##                   927       928       932       937       939       943
## Predicted    7577.215  9482.581  9280.411 9200.3920 10097.646  7864.805
## cvpred       8681.178  9525.935  9456.778 9303.3131 10116.624  8072.078
## price        5203.000 15704.000 14000.000 9000.0000 10682.000  6000.000
## CV residual -3478.178  6178.065  4543.222 -303.3131   565.376 -2072.078
##                   944       946       947       953       956      1073
## Predicted    8177.273 10320.502  9091.835  8793.267 8430.6094 9076.1909
## cvpred       8414.958 10170.927  9214.261  9064.251 8636.4333 9162.4577
## price       10999.000  6759.000  5900.000  5300.000 8000.0000 9500.0000
## CV residual  2584.042 -3411.927 -3314.261 -3764.251 -636.4333  337.5423
##                  1079      1087      1098      1100      1105      1109
## Predicted   10308.762  9485.970  8556.340  9890.885  8945.135  8362.750
## cvpred      10632.538  9589.439  9177.315  9868.084  8984.556  8451.503
## price        7500.000  7229.000  5786.000  5857.000  5500.000  5081.000
## CV residual -3132.538 -2360.439 -3391.315 -4011.084 -3484.556 -3370.503
##                  1119      1124      1128      1131      1133      1135
## Predicted    8855.032 7633.8130 8883.0774  8306.257  9630.087  9531.615
## cvpred       8952.708 7824.1989 8949.7893  8414.385  9558.867  9509.372
## price       11618.000 8500.0000 8614.0000  6139.000 13586.000  5786.000
## CV residual  2665.292  675.8011 -335.7893 -2275.385  4027.133 -3723.372
##                  1136      1143      1147      1148      1150      1154
## Predicted    9621.674 7666.8222  8956.264 10180.422  9600.573  9033.635
## cvpred       9566.506 7841.5765  8979.854 10120.136  9555.900  9018.743
## price        5266.000 6888.0000  5500.000  5435.000  7950.000  6542.000
## CV residual -4300.506 -953.5765 -3479.854 -4685.136 -1605.900 -2476.743
##                  1164      1166      1168      1172      1174      1181
## Predicted    9019.657 10294.252  8957.733  8889.179  9011.378  8982.239
## cvpred       9028.733 10148.467  8985.741  8982.168  9028.146  8993.697
## price        7500.000  8816.000 12675.000  6000.000  7014.000  7000.000
## CV residual -1528.733 -1332.467  3689.259 -2982.168 -2014.146 -1993.697
##                  1182      1198      1285     1290      1291      1292
## Predicted    8992.992  8712.288 11513.578 15766.79 10423.956 10252.652
## cvpred       9020.477  8898.763 11509.724 15262.44 10162.876 11442.619
## price       10500.000  6500.000  6400.000 25454.00  6280.000  6660.000
## CV residual  1479.523 -2398.763 -5109.724 10191.56 -3882.876 -4782.619
##                  1293      1295      1299      1302      1306      1308
## Predicted    7624.236 12367.717 8604.0169 8852.3739  9572.824  8141.139
## cvpred       8760.105 12283.487 8950.3095 9096.1314  9840.401  8628.661
## price        7504.000 12390.000 9500.0000 9575.0000  7200.000 10000.000
## CV residual -1256.105   106.513  549.6905  478.8686 -2640.401  1371.339
##                  1310      1312       1318      1320      1322     1324
## Predicted   10387.688 10561.047  9563.4883 10464.935  9127.772 10920.48
## cvpred      10411.197 10202.112  9763.7814 10522.661  9179.061 10797.00
## price        8454.000 12169.000 10000.0000  8000.000  7857.000  7579.00
## CV residual -1957.197  1966.888   236.2186 -2522.661 -1322.061 -3218.00
##                  1326      1327      1330      1336      1342      1383
## Predicted   13153.129  8958.598  8251.479  8164.552  7016.117  9324.232
## cvpred      12457.205  9068.536  8399.179  8325.174  8150.288  9477.129
## price       20343.000  5100.000  6429.000  5877.000  5113.000  7500.000
## CV residual  7885.795 -3968.536 -1970.179 -2448.174 -3037.288 -1977.129
##                    1385      1386      1389      1391      1394      1395
## Predicted   9447.255390  9871.539  8796.513 8158.4589 8326.5782  7559.847
## cvpred      9509.294221 10009.566  8907.066 8323.0833 8413.5182  7782.660
## price       9500.000000  5486.000 11500.000 8657.0000 9082.0000  5500.000
## CV residual   -9.294221 -4523.566  2592.934  333.9167  668.4818 -2282.660
##                  1396      1397      1398      1400      1401      1403
## Predicted   11271.226  8471.802 10219.506 8207.6949 10845.563 10128.068
## cvpred      11144.704  8190.292 10095.455 8347.8306 10655.606 10049.496
## price        8800.000 18018.000  5365.000 8080.0000 16429.000 16000.000
## CV residual -2344.704  9827.708 -4730.455 -267.8306  5773.394  5950.504
##                  1404      1408      1411      1414      1420      1422
## Predicted    8221.762  8013.204 10668.474  8981.460  8190.178 11333.150
## cvpred       8354.901  9146.911 10637.804  8982.224  8368.695 11187.696
## price        7143.000  5500.000  9000.000  7117.000  7314.000 14200.000
## CV residual -1211.901 -3646.911 -1637.804 -1865.224 -1054.695  3012.304
##                  1423      1429      1430      1436      1439      1440
## Predicted   10662.821  8786.720  8319.544  8872.504  9549.177  8297.063
## cvpred      10623.094  8925.879  8409.983  8957.129  9530.853  8410.551
## price       15000.000  5221.000  5999.000  5356.000  5352.000  6000.000
## CV residual  4376.906 -3704.879 -2410.983 -3601.129 -4178.853 -2410.551
##                  1441      1452      1454      1459     1461      1466
## Predicted    7968.932  8816.925  9698.265  8341.336 12751.87 8964.2183
## cvpred       9142.460  8923.259  9593.921  8415.002 12350.20 8683.2715
## price        5500.000  6400.000  8466.000  5999.000 28514.00 8500.0000
## CV residual -3642.460 -2523.259 -1127.921 -2416.002 16163.80 -183.2715
##                  1467      1821      1822      1824      1913      1921
## Predicted   10261.708  6217.515  6990.267 10772.159 6910.6191  6927.446
## cvpred      10116.667  7621.432  8420.281 11288.952 7228.6646  7213.387
## price        7227.000  6200.000 10000.000  5110.000 7360.0000  6187.000
## CV residual -2889.667 -1421.432  1579.719 -6178.952  131.3354 -1026.387
##                  1923      2206      2207      2218     2265       2269
## Predicted   6338.1873  8715.799  9613.753  5984.612  6987.71 7059.18041
## cvpred      7515.1628  8805.151  9986.080  6954.802  7012.73 7182.05871
## price       6615.0000  5120.000 15000.000 10000.000  5455.00 7201.00000
## CV residual -900.1628 -3685.151  5013.920  3045.198 -1557.73   18.94129
##                  2270      2305      2307        2318      2320      2325
## Predicted   7217.9276 12672.517  9623.054 10271.08079  8598.127  9618.269
## cvpred      7166.9073 12345.134  9555.332 10154.62209  8944.260  9569.155
## price       7413.0000 10000.000  6500.000 10238.00000 12500.000  5474.000
## CV residual  246.0927 -2345.134 -3055.332    83.37791  3555.740 -4095.155
##                 2327      2329      2332     2335      2336      2337      2339
## Predicted   8338.710  9025.445  9652.658 8238.769  8985.868  8270.156  8773.199
## cvpred      8429.125  9035.217  9575.359 8373.744  8999.882  8425.553  9127.699
## price       9500.000  6857.000  7500.000 7856.000 10000.000  5059.000  7314.000
## CV residual 1070.875 -2178.217 -2075.359 -517.744  1000.118 -3366.553 -1813.699
##                  2345      2346      2350      2353      2354      2358
## Predicted    8987.338  9545.996  8311.203  9869.872  9216.836 8359.8114
## cvpred       9005.768  9542.338  8466.774 10069.282  9474.981 8439.7307
## price        8000.000 10304.000  5888.000 13000.000 14545.000 8571.0000
## CV residual -1005.768   761.662 -2578.774  2930.718  5070.019  131.2693
##                  2377      2378      2380      2381      2382       2384
## Predicted   10444.910  8192.248  9051.797  8777.616 8099.2836 10936.3114
## cvpred      10572.905  8351.934  9017.577  8939.105 8121.7315 10707.1528
## price        8643.000  6500.000 23334.000  5083.000 8569.0000 11564.0000
## CV residual -1929.905 -1851.934 14316.423 -3856.105  447.2685   856.8472
##                  2393      2395      2396     2397      2402      2409
## Predicted    7687.554  7441.232  7694.178 7785.616 10165.441  9448.169
## cvpred       7580.299  7835.785  7844.245 7890.204 10109.818  9512.542
## price        5198.000  5800.000  5800.000 8990.000 19988.000  5500.000
## CV residual -2382.299 -2035.785 -2044.245 1099.796  9878.182 -4012.542
##                  2412      2440       2441      2442      2458      2472
## Predicted    9611.925  8885.927 8890.89066  9096.938  9500.031  9369.195
## cvpred       9560.033  8944.501 8964.79776  9050.561  9523.166  9475.993
## price       13714.000  5500.000 9000.00000  7082.000 14455.000  7293.000
## CV residual  4153.967 -3444.501   35.20224 -1968.561  4931.834 -2182.993
##                  2507      2508      2513      2522      2524     2525
## Predicted    8930.244 11557.808 8865.1840  8909.967  8884.771 8302.072
## cvpred       8991.298 11289.963 9002.1362  8966.879  8964.510 8405.562
## price        5829.000  8000.000 8214.0000  7600.000  6500.000 8824.000
## CV residual -3162.298 -3289.963 -788.1362 -1366.879 -2464.510  418.438
##                  2526      2528      2546      2552      2556      2561
## Predicted    8948.074  9467.712  9674.539  8413.456  9092.844  9068.803
## cvpred       8996.328  9500.202  9597.438  8482.136  9058.798  9036.420
## price        6000.000  7571.000 10993.000 10000.000 25857.000 10143.000
## CV residual -2996.328 -1929.202  1395.562  1517.864 16798.202  1106.580
##                  2570      2573     2575      2578      2622      2631
## Predicted    8203.600 10795.126 8938.657  8330.800  8911.302  9088.749
## cvpred       8356.067 10676.154 8983.659  8902.835  8980.991  9067.035
## price        6000.000 12679.000 8000.000  5870.000  6786.000  7500.000
## CV residual -2356.067  2002.846 -983.659 -3032.835 -2194.991 -1567.035
##                   2634      2637       2641      2645      2648      2649
## Predicted    9767.2943  8861.197 9079.08979 9705.1467 10275.776  8882.477
## cvpred       9689.6004  8927.710 9077.62228 9637.7734 10123.738  8972.437
## price       10030.0000 11419.000 9000.00000 9003.0000 11660.000  6000.000
## CV residual   340.3996  2491.290  -77.62228 -634.7734  1536.262 -2972.437
##                  2655      2656      2661      2663      2664      2666
## Predicted    9595.232  8949.230  8330.207  9200.760  8843.724  8878.893
## cvpred       9567.085  8976.319  8419.703  9195.399  8923.289  8940.966
## price        7871.000  6500.000  6500.000  7500.000 15000.000  6000.000
## CV residual -1696.085 -2476.319 -1919.703 -1695.399  6076.711 -2940.966
##                  2667      2787       2792      2793      2796      2797
## Predicted   8449.7802  9552.520 10253.3957  8367.058 10324.081 8834.2914
## cvpred      8479.8039  9625.246 10205.7159  8548.926 10216.994 8976.7732
## price       8357.0000  7320.000 11000.0000  5329.000 15400.000 9429.0000
## CV residual -122.8039 -2305.246   794.2841 -3219.926  5183.006  452.2268
##                  2799      2800     2805      2806       2807      2808
## Predicted    9015.697  9627.687 9613.619  9921.993  9024.2007  8533.602
## cvpred       9068.409  9621.490 9614.419  9965.536  9077.8305  8727.836
## price        7900.000 12240.000 9500.000 14900.000 10000.0000  5200.000
## CV residual -1168.409  2618.510 -114.419  4934.464   922.1695 -3527.836
##                  2814      2822      2823      2826      2829      2836
## Predicted    8801.079 10321.949 14315.307 11161.498  8892.248 10122.752
## cvpred       8991.320 10330.798 13937.408 11020.304  9107.608 10223.442
## price        6299.000  6000.000  8800.000 17530.000  6500.000 14750.000
## CV residual -2692.320 -4330.798 -5137.408  6509.696 -2607.608  4526.558
##                  2839      2840      2841      2843      2883      2890
## Predicted   10014.231 10269.920  9650.470  9607.225  9033.899  9549.216
## cvpred      10239.991 10228.893  9780.217  9645.179  9124.186  9587.796
## price       11429.000 13337.000 14950.000  8000.000  6973.000 15500.000
## CV residual  1189.009  3108.107  5169.783 -1645.179 -2151.186  5912.204
##                  2933       2935      2958      2965      2967      2968
## Predicted    9569.361 10870.0457 8196.5665  9781.514  8905.558  8224.011
## cvpred      10098.360 11154.9849 8352.5321  9656.354  8949.221  8372.260
## price        8000.000 10800.0000 7800.0000  7429.000  6000.000  6423.000
## CV residual -2098.360  -354.9849 -552.5321 -2227.354 -2949.221 -1949.260
##                  2970        2976      2978      2991      2992      2993
## Predicted   10257.614 10174.72326  8874.798  8262.674  8616.199  8896.634
## cvpred      10124.904 10130.71215  8949.203  8404.348  8926.034  8996.567
## price        8000.000 10201.00000 17500.000  6500.000  5022.000  7714.000
## CV residual -2124.904    70.28785  8550.797 -1904.348 -3904.034 -1282.567
##                  2998      3000      3002      3004      3005     3007
## Predicted   8173.4851  8783.826 10323.166  9082.871  8959.758 8188.063
## cvpred      8375.7476  8888.822 10174.081  9043.490  8994.265 8343.111
## price       8000.0000  5750.000 15000.000  5457.000  5162.000 9381.000
## CV residual -375.7476 -3138.822  4825.919 -3586.490 -3832.265 1037.889
##                  3012      3206      3211      3219      3243      3245
## Predicted    9043.608  9757.570  9116.918  8434.216  8180.100 7137.5662
## cvpred       9034.051  9769.647  9192.380  8675.094  8402.481 7444.8982
## price        7500.000  6000.000  5300.000  6500.000  6250.000 7628.0000
## CV residual -1534.051 -3769.647 -3892.380 -2175.094 -2152.481  183.1018
##                  3289      3292      3311     3319      3326      3331
## Predicted    8851.493 11487.157  8171.926 7611.332 7640.8467  7663.417
## cvpred       8963.583 11228.714  8352.801 7824.767 7827.7342  7844.226
## price        5162.000  9900.000 13600.000 7214.000 8625.0000  5300.000
## CV residual -3801.583 -1328.714  5247.199 -610.767  797.2658 -2544.226
##                  3333      3334      3345      3363      3366      3367
## Predicted   7695.6470  7683.049  8214.307  6895.951  6810.167  9002.561
## cvpred      7850.1307  7848.946  8408.134  7244.241  7212.991  8992.830
## price       7636.0000  6564.000  5899.000 10000.000 10000.000  5782.000
## CV residual -214.1307 -1284.946 -2509.134  2755.759  2787.009 -3210.830
##                  3368      3369      3370      3372      3440      3448
## Predicted   10804.830  8903.578  9122.742 6973.9225  8249.297  7670.451
## cvpred      10640.281  8983.043  9501.479 7260.4825  8391.690  7847.762
## price       13065.000  7738.000  5750.000 7406.0000  5229.000 26526.000
## CV residual  2424.719 -1245.043 -3751.479  145.5175 -3162.690 18678.238
## 
## Sum of squares = 4995454715    Mean square = 14032176    n = 356 
## 
## fold 3 
## Observations in test set: 356 
##                   112       115      123       125       129       141
## Predicted    8200.061 7582.4176 8925.970  8870.390 8247.9117  8478.039
## cvpred       7969.928 7312.4682 8713.436  8779.034 8132.6773  8096.572
## price       10000.000 6500.0000 9800.000  5372.000 9000.0000 13520.000
## CV residual  2030.072 -812.4682 1086.564 -3407.034  867.3227  5423.428
##                   145       146       169       173       174      182
## Predicted    7893.253  9943.198 8339.3893 10296.473  8730.233 10661.24
## cvpred       7473.435  9076.523 8050.2305 10272.051  8263.317 10605.27
## price        6000.000 13285.000 8182.0000  9064.000  5915.000  8999.00
## CV residual -1473.435  4208.477  131.7695 -1208.051 -2348.317 -1606.27
##                   189        196       197       214       220      234
## Predicted    8892.131 8306.20630  8161.095  7557.614  9034.077 8145.843
## cvpred       8835.411 7981.28176  8185.087  7194.223  8422.830 7522.462
## price       10325.000 8053.00000 12390.000  6131.000  5940.000 8803.000
## CV residual  1489.589   71.71824  4204.913 -1063.223 -2482.830 1280.538
##                   286       290       292       306       308       309
## Predicted   9526.0511 10153.577  9544.806 8821.1538  8810.581  8844.459
## cvpred      9494.3384 10224.651  9092.706 8805.2969  8696.862  8541.215
## price       8500.0000  9419.000  6599.000 9280.0000  6000.000 12000.000
## CV residual -994.3384  -805.651 -2493.706  474.7031 -2696.862  3458.785
##                   310       313       325       326       328       329
## Predicted    8858.437 8372.0423  8084.072 8161.3529  8268.239  8201.530
## cvpred       8599.434 7680.5391  7852.048 7876.5001  7891.385  7975.369
## price        5640.000 6899.0000  5800.000 7434.0000  6800.000  6109.000
## CV residual -2959.434 -781.5391 -2052.048 -442.5001 -1091.385 -1866.369
##                  357      363      368       371       382       388       389
## Predicted   7429.880 7465.138 6590.096  6728.567  6978.241  7571.934  8458.623
## cvpred      7142.185 7057.702 6093.694  6271.481  6546.200  7138.310  7491.083
## price       9280.000 8900.000 9999.000 22556.000 10219.000  5500.000 23904.000
## CV residual 2137.815 1842.298 3905.306 16284.519  3672.800 -1638.310 16412.917
##                   395       398       400       406       407       410
## Predicted    9566.094  9572.348  8196.566 8169.0766 8174.0405  7975.116
## cvpred       9430.804  9457.193  8085.867 7908.3302 7797.8323  7730.417
## price        6204.000 13098.000  6000.000 7000.0000 7000.0000  5162.000
## CV residual -3226.804  3640.807 -2085.867 -908.3302 -797.8323 -2568.417
##                   412       413       416      432       436       437
## Predicted    9452.775 7920.2710  9493.687 11945.19  8905.738  8934.562
## cvpred       9520.975 7537.7476  9361.577  9146.90  8628.828  8649.403
## price        5828.000 7000.0000  6486.000  7899.00  6000.000  5286.000
## CV residual -3692.975 -537.7476 -2875.577 -1247.90 -2628.828 -3363.403
##                   440       442        445       450       451       453
## Predicted    9077.307 8783.6737  8641.0240 10980.987 9704.8330  9029.540
## cvpred       8681.110 8875.0895  9279.0199 10860.792 9411.4227  8712.815
## price        5500.000 9500.0000 10000.0000  7400.000 8892.0000 27438.000
## CV residual -3181.110  624.9105   720.9801 -3460.792 -519.4227 18725.185
##                   493       494       496      497       498      501       512
## Predicted    9525.361 7739.3188  9631.557  8314.76  8842.345 8250.766  8855.722
## cvpred       9458.756 7270.9491  9438.060  7950.92  8728.318 7949.105  8685.233
## price       15116.000 6435.0000 14036.000  6525.00  7500.000 9781.000 13000.000
## CV residual  5657.244 -835.9491  4597.940 -1425.92 -1228.318 1831.895  4314.767
##                   513       522       523       529       532       533
## Predicted    8897.234 11584.339  8983.243  9528.990 8392.3547  9536.024
## cvpred       8627.139 11429.075  8749.960  9505.221 8006.3294  9501.469
## price        5500.000  8000.000  6000.000  7000.000 8500.0000 12186.000
## CV residual -3127.139 -3429.075 -2749.960 -2505.221  493.6706  2684.531
##                   535      547       550       552       556       557
## Predicted    8451.877 10230.95  9082.871  9106.911  8990.142  8220.562
## cvpred       8018.154 10183.38  8671.917  8671.544  8583.805  7857.367
## price       25000.000  7848.00 26000.000  5343.000  6000.000  5929.000
## CV residual 16981.846 -2335.38 17328.083 -3328.544 -2583.805 -1928.367
##                   558       571       574       580       582       586
## Predicted   8309.1059  9567.563  9050.641 9592.9385  8001.916 8854.4318
## cvpred      8025.8359  9436.245  8701.559 9278.9093  7872.372 8548.3457
## price       8014.0000  6000.000  6500.000 9077.0000  5123.000 9318.0000
## CV residual  -11.8359 -3436.245 -2201.559 -201.9093 -2749.372  769.6543
##                   588       591      598       602       615       619
## Predicted    8943.666  9035.732 11457.73  9513.453  9590.824 9032.2549
## cvpred       8752.397  8765.537 11496.61  9507.283  9466.012 8627.0165
## price        6468.000 15000.000 25000.00 10734.000  7911.000 9555.0000
## CV residual -2284.397  6234.463 13503.39  1226.717 -1555.012  927.9835
##                   628       632         634       635       703       704
## Predicted    9637.211 11947.343 8421.959083 10027.105  9560.198  9029.540
## cvpred       9363.144 12444.288 7996.762815  9932.614  9141.524  8712.815
## price       12600.000 10850.000 8000.000000 11211.000 12400.000  6909.000
## CV residual  3236.856 -1594.288    3.237185  1278.386  3258.476 -1803.815
##                   707       710       712       714       718       723
## Predicted   9078.7761  8703.184  9567.098 9001.4052  9036.574  8786.765
## cvpred      8686.5513  8514.949  9497.343 8727.8224  8709.063  8793.916
## price       8900.0000  7000.000  5400.000 8000.0000  6229.000  5250.000
## CV residual  213.4487 -1514.949 -4097.343 -727.8224 -2480.063 -3543.916
##                   725       728       729       732       733      741
## Predicted   8266.9036  8983.243  9631.557 10232.418 8319.0786 8140.297
## cvpred      8048.3474  8749.960  9438.060 10188.821 8032.9663 8115.882
## price       7286.0000  5300.000  7000.000 13653.000 9000.0000 8000.000
## CV residual -762.3474 -3449.960 -2438.060  3464.179  967.0337 -115.882
##                   742       743       748       767       768       770
## Predicted    9018.412  8955.108  9531.615  7914.017  8889.421  7744.883
## cvpred       8731.201  8764.968  9485.145  7511.359  8661.032  7261.756
## price        7532.000 12400.000 15000.000 11000.000  5300.000 24175.000
## CV residual -1199.201  3635.032  5514.855  3488.641 -3361.032 16913.244
##                  773       775      777       781       783        784
## Predicted   11255.18 8286.5353 8504.580 7618.2761  8377.284 8298.53288
## cvpred      11382.73 8031.6505 7915.341 7329.2906  7947.294 7917.40072
## price       19800.00 7500.0000 7714.000 6600.0000  6000.000 8000.00000
## CV residual  8417.27 -531.6505 -201.341 -729.2906 -1947.294   82.59928
##                   791       800       801       811       889       895
## Predicted    9531.615  8221.852  8170.546  9626.638  9236.682 8532.7125
## cvpred       9485.145  7994.254  7913.771  9254.709  7891.905 7774.7504
## price       25000.000  5358.000 13857.000  8056.000 18518.000 8500.0000
## CV residual 15514.855 -2636.254  5943.229 -1198.709 10626.095  725.2496
##                   897       899       901       904      907       910
## Predicted   9028.4514  9658.244  9551.539 14093.783 10523.03 10738.274
## cvpred      8667.3182  8909.510  9386.367 14803.474 11121.96 10611.131
## price       9286.0000  5800.000 12342.000  9566.000  7000.00  5500.000
## CV residual  618.6818 -3109.510  2955.633 -5237.474 -4121.96 -5111.131
##                   912       917       920       922       925       926
## Predicted    7920.421  8865.555  9358.852 8819.7624  9626.505  9578.885
## cvpred       7459.819  8790.137  8884.649 8730.4637  9226.472 10167.563
## price       20000.000  6195.000  6429.000 9329.0000 10500.000  7000.000
## CV residual 12540.181 -2595.137 -2455.649  598.5363  1273.528 -3167.563
##                   930       935      940       941      948      1071      1072
## Predicted   10044.758  8642.136 8355.046 11088.278 10495.64  9319.252 11234.471
## cvpred       9660.069  8176.363 7863.773 12220.095 10289.44  8771.998 11164.424
## price       11335.000 18571.000 7000.000  7900.000 26474.00 10670.000  5286.000
## CV residual  1674.931 10394.637 -863.773 -4320.095 16184.56  1898.002 -5878.424
##                  1075      1077      1101      1106      1107      1113
## Predicted    9071.917  9627.556 10279.477  8240.238 10208.467 9014.0032
## cvpred       8821.083  8917.832  9854.019  8068.796 10123.472 8714.8774
## price        6500.000 14500.000  7300.000 13000.000  7771.000 8000.0000
## CV residual -2321.083  5582.168 -2554.019  4931.204 -2352.472 -714.8774
##                   1118      1120      1129      1134      1137      1149
## Predicted   10230.9483  8857.792  8926.660  9670.910 7723.7819 10107.746
## cvpred      10183.3799  8791.978  8749.018  9338.943 7273.0118 10200.698
## price       10410.0000 17143.000  6800.000 25300.000 7168.0000  8900.000
## CV residual   226.6201  8351.022 -1949.018 15961.057 -105.0118 -1300.698
##                  1156      1158      1163       1167      1169      1171
## Predicted    9007.059  9540.898  8238.769  9665.5696  8980.618  8962.142
## cvpred       8652.906  9456.694  8063.355  9444.8165  8770.036  8761.216
## price        5800.000  5357.000 17500.000 10200.0000  6000.000  5500.000
## CV residual -2852.906 -4099.694  9436.645   755.1835 -2770.036 -3261.216
##                  1178      1185      1197      1279      1281      1287
## Predicted    8903.247 10753.614  9413.135 11267.924  9469.327  9147.292
## cvpred       8811.307 10777.427  9027.770 12303.541  9176.944  9719.010
## price        6000.000 17243.000  6000.000 14167.000 15985.000  8173.000
## CV residual -2811.307  6465.573 -3027.770  1863.459  6808.056 -1546.010
##                  1289      1294      1297     1298       1301     1304
## Predicted    9661.648  7638.304 12425.840 11197.59  9854.1692 11290.88
## cvpred       8859.293  7407.642 13659.731 12341.06 10580.5203 11148.48
## price        5723.000 13100.000  8970.000  6680.00  9990.0000  7999.00
## CV residual -3136.293  5692.358 -4689.731 -5661.06  -590.5203 -3149.48
##                  1311      1313      1315      1316      1325      1328
## Predicted   10410.169  9057.597  9365.893  9000.166 10335.249 7783.8551
## cvpred      10296.301  8876.996  9997.854  8560.933 10186.717 7420.2405
## price        8599.000 13575.000  6520.000  7000.000 11757.000 7143.0000
## CV residual -1697.301  4698.004 -3477.854 -1560.933  1570.283 -277.2405
##                  1333      1335      1337      1339      1340      1375
## Predicted    9150.373 14402.078 10905.214  9012.976  9012.976  8582.876
## cvpred       8807.474 15814.535 10601.196  8434.085  8434.085  8315.023
## price       10000.000  8400.000 19562.000 15000.000 15000.000  5314.000
## CV residual  1192.526 -7414.535  8960.804  6565.915  6565.915 -3001.023
##                  1381      1390      1392      1393      1405      1406
## Predicted    8816.925 10104.207  9544.213  9079.932  9023.662  8953.325
## cvpred       8657.528 10088.511  9472.200  8661.035  8691.050  8728.569
## price        6500.000  8900.000  7500.000  5250.000 10000.000 14429.000
## CV residual -2157.528 -1188.511 -1972.200 -3411.035  1308.950  5700.431
##                  1410      1412       1413      1415     1416      1417
## Predicted   10203.369 7975.8508 8799.40742  8519.017 7594.326 8804.3713
## cvpred      10071.566 7472.1503 8487.12176  7953.637 7263.941 8376.6239
## price        5980.000 8000.0000 8529.00000 11900.000 8500.000 8110.0000
## CV residual -4091.566  527.8497   41.87824  3946.363 1236.059 -266.6239
##                  1419      1421      1424      1427      1428      1431
## Predicted   8482.3345  8742.448  9570.968  9505.595  7680.110 8918.1564
## cvpred      8260.8044  8481.555  9386.029  9313.050  7290.082 8747.3289
## price       8500.0000  6300.000 12826.000 15073.000  5990.000 8129.0000
## CV residual  239.1956 -2181.555  3439.971  5759.950 -1300.082 -618.3289
##                  1433      1434      1435      1443        1446      1447
## Predicted    8900.639 10057.865  9450.015  9520.352 9371.954347 11405.557
## cvpred       8576.923  9897.531  9378.647  9341.128 9384.336538 11511.991
## price       15086.000 17962.000  5500.000 15514.000 9390.000000 18900.000
## CV residual  6509.077  8064.469 -3878.647  6172.872    5.663462  7388.009
##                  1449      1450      1451      1462      1463      1464
## Predicted   11975.344  8929.464  9570.278  9572.348  8278.032  8158.459
## cvpred      12266.878  8597.497  9350.447  9457.193  8029.961  8093.744
## price       11050.000  5280.000  5473.000 15514.000 13800.000  6000.000
## CV residual -1216.878 -3317.497 -3877.447  6056.807  5770.039 -2093.744
##                  1468      1763      1839      1841     1906     1915      1916
## Predicted   7539.4357  7081.413  7033.849  7822.818 6973.643 7061.087  7177.486
## cvpred      7365.1205  6535.664  6339.316  8344.787 7510.764 6561.459  7761.530
## price       7000.0000 10000.000 10000.000 11644.000 9999.000 8318.000  6000.000
## CV residual -365.1205  3464.336  3660.684  3299.213 2488.236 1756.541 -1761.530
##                  2131      2180      2205      2220      2271      2298
## Predicted    7564.909  7325.637 6794.0742  7049.269 8127.3323  9438.107
## cvpred       7871.211  7616.351 5984.8881  6544.263 8138.1998  9427.174
## price       11644.000  5750.000 5100.0000 13900.000 9000.0000  7527.000
## CV residual  3772.789 -1866.351 -884.8881  7355.737  861.8002 -1900.174
##                  2299       2309      2311      2312      2314      2315
## Predicted    8638.546  9571.0578 11432.357  9481.089  8838.160 11020.564
## cvpred       8183.703  9320.3059 11653.945  9374.522  8808.675 10858.356
## price       14000.000 10000.0000 20750.000 15656.000 10500.000 16000.000
## CV residual  5816.297   679.6941  9096.055  6281.478  1691.325  5141.644
##                  2319      2338      2340      2342      2343       2344
## Predicted    8990.277  8765.977  8928.443  8970.824  9659.692 8761.52398
## cvpred       8746.209  8314.154  8785.417  8631.460  9423.052 8591.67954
## price       15000.000  6533.000 12000.000  5500.000  6500.000 8500.00000
## CV residual  6253.791 -1781.154  3214.583 -3131.460 -2923.052  -91.67954
##                  2347      2370      2375      2383      2386      2389
## Predicted    9652.972  8834.576  8167.697  8798.583 10226.540 7448.2660
## cvpred       9457.762  8468.362  7837.166  8811.112 10167.056 6694.7519
## price        8000.000  5255.000  6508.000 19998.000  6499.000 5800.0000
## CV residual -1457.762 -3213.362 -1329.166 11186.888 -3668.056 -894.7519
##                  2391    2394      2399      2403      2411     2413      2433
## Predicted   7466.1930 6499.52  7680.110  9678.264  8858.571 10315.35  8248.741
## cvpred      7947.3499 5043.83  7290.082 10483.106  8761.838 10138.36  8070.485
## price       7198.0000 6200.00  5990.000  8013.000  7095.000 22500.00 13338.000
## CV residual -749.3499 1156.17 -1300.082 -2470.106 -1666.838 12361.64  5267.515
##                  2443      2445      2446      2456      2460      2462
## Predicted   10122.593  8968.262  9602.732 10184.427 10213.942 10412.586
## cvpred      10163.054  8625.202  9417.485 10123.845 10180.001 11294.026
## price       16894.000 13700.000  6500.000 14321.000  6971.000  8000.000
## CV residual  6730.946  5074.798 -2917.485  4197.155 -3209.001 -3294.026
##                  2464      2473      2474      2487      2506      2511
## Predicted   11379.492  8234.450 12533.823 10154.312  8876.268  8456.124
## cvpred      11633.744  7981.309 13171.596  9966.384  8800.798  7911.464
## price       15941.000  6000.000  6836.000 12300.000  5300.000  6620.000
## CV residual  4307.256 -1981.309 -6335.596  2333.616 -3500.798 -1291.464
##                  2515      2517      2519      2523      2527      2529
## Predicted    7562.786  9711.867  8896.213  8561.630  8223.546 10785.199
## cvpred       7329.165  9407.671  8815.059  7855.185  8096.375 10940.329
## price        5800.000 26302.000  7500.000  5001.000  6714.000  8143.000
## CV residual -1529.165 16894.329 -1315.059 -2854.185 -1382.375 -2797.329
##                  2530      2531      2537     2538      2539      2541     2543
## Predicted    8798.583 11585.718  9063.239 10195.78  8857.882 10226.854 7678.954
## cvpred       8811.112 11500.239  8688.614 10202.14  8726.256 10198.014 7315.599
## price        6286.000  6929.000  5312.000 17900.00  5500.000  8631.000 8654.000
## CV residual -2525.112 -4571.239 -3376.614  7697.86 -3226.256 -1567.014 1338.401
##                   2544      2547      2558      2566       2568      2574
## Predicted   10797.1066  9765.197  8410.517  8970.331 10097.3077 8292.2787
## cvpred      10891.8025  9366.773  7984.191  8731.948 10254.6664 7891.0118
## price       10721.0000 20000.000 26000.000  7357.000 10933.0000 7113.0000
## CV residual  -170.8025 10633.227 18015.809 -1374.948   678.3336 -778.0118
##                  2576      2621      2624      2626      2627       2628
## Predicted    8358.342  9611.925  8183.969 8969.1756  8465.407 8265.88210
## cvpred       7999.572  9454.757  8098.812 8757.4643  7883.012 7714.29213
## price        5500.000  5800.000  6200.000 8500.0000 14545.000 7700.00000
## CV residual -2499.572 -3654.757 -1898.812 -257.4643  6661.988  -14.29213
##                  2629      2644      2651     2659      2781      2782
## Predicted   10236.513  8978.145  8966.702 8948.074 10170.943  9517.352
## cvpred      10174.187  8698.055  8685.483 8768.720  9967.187  9358.628
## price        7500.000  5580.000  6000.000 9500.000  7600.000  8160.000
## CV residual -2674.187 -3118.055 -2685.483  731.280 -2367.187 -1198.628
##                  2783      2784      2788      2789      2798      2801
## Predicted   10377.137 8706.4825  8833.438  8975.335 8347.4383 10283.348
## cvpred       9828.819 8264.9883  8456.965  8587.778 8116.6875 10266.728
## price       11714.000 9000.0000 11650.000  7227.000 8325.0000  9000.000
## CV residual  1885.181  735.0117  3193.035 -1360.778  208.3125 -1266.728
##                  2809      2810      2815      2817      2821      2884
## Predicted    9641.754  9174.040  9333.567  9717.128  9354.422  9117.109
## cvpred       9543.919  9037.856  8978.310  9478.938  8865.084  8889.248
## price        7200.000  5914.000  5098.000  6500.000  7857.000  5032.000
## CV residual -2343.919 -3123.856 -3880.310 -2978.938 -1008.084 -3857.248
##                  2885       2888     2889      2907     2912     2929      2934
## Predicted   9050.0363 10132.6828 8350.153  7789.425  8420.49 8462.126  9620.826
## cvpred      8862.4796  9750.4091 8030.889  7260.667  7993.37 8096.059  8952.969
## price       7950.0000 10000.0000 9292.000  5036.000  6688.00 8000.000 10856.000
## CV residual -912.4796   249.5909 1261.111 -2224.667 -1305.37  -96.059  1903.031
##                  2959      2960      2962      2963      2971      2972
## Predicted   10348.452  9481.089  8911.902  9004.344  8981.460 8276.8763
## cvpred      10012.851  9374.522  8720.940  8738.705  8713.562 8055.4778
## price        6306.000  5454.000  5317.000  6571.000 14500.000 7500.0000
## CV residual -3706.851 -3920.522 -3403.940 -2167.705  5786.438 -555.4778
##                  2974      2977      2979      2981      2983      2997
## Predicted    8953.504  9574.131  8960.672  8410.517 9441.6465 10159.142
## cvpred       8597.124  9493.591  8755.775  7984.191 9539.3615 10215.458
## price        6000.000 22500.000 15000.000  6000.000 9000.0000  9053.000
## CV residual -2597.124 13006.409  6244.225 -1984.191 -539.3615 -1162.458
##                  3001      3008      3009      3010      3215      3216
## Predicted    8939.661  8914.062  9486.788  8327.582  8868.073  8809.044
## cvpred       8701.308  8761.963  9527.732  8034.655  8570.317  8458.004
## price        5100.000  5500.000  6000.000  5100.000 11211.000 11423.000
## CV residual -3601.308 -3261.963 -3527.732 -2934.655  2640.683  2964.996
##                  3218      3221      3222      3225      3236      3238
## Predicted    8432.146  8464.421  8445.081  8284.550 8472.9014  9065.151
## cvpred       8103.050  8301.534  8126.352  8119.359 7775.9578  8418.704
## price        6500.000  6500.000  6950.000  5143.000 7136.0000  5162.000
## CV residual -1603.050 -1801.534 -1176.352 -2976.359 -639.9578 -3256.704
##                  3242      3293      3294      3307       3308      3312
## Predicted   7752.4331  9697.575  9441.646 8305.0112 8330.20707  8702.350
## cvpred      7274.6517  9318.494  9539.361 8040.4701 8014.58014  8170.897
## price       6500.0000  6200.000  6190.000 7334.0000 8000.00000  6000.000
## CV residual -774.6517 -3118.494 -3349.361 -706.4701  -14.58014 -2170.897
##                  3314      3316      3317      3329      3332     3344     3365
## Predicted    8312.045  8407.578  8230.266 7648.6600  7567.571 7702.681 6956.361
## cvpred       8036.718  7973.309  8061.666 7289.5832  7350.113 7284.268 6587.597
## price        6499.000  6214.000  6000.000 7500.0000  5895.000 8300.000 8000.000
## CV residual -1537.718 -1759.309 -2061.666  210.4168 -1455.113 1015.732 1412.403
##                  3371      3375      3377     3379      3438      3449
## Predicted    6910.019  8506.050  9568.253 7009.226  7552.813 7526.8378
## cvpred       6396.616  7920.782  9471.827 6607.798  7322.035 7378.0655
## price       10000.000  5785.000  7827.000 9000.000 10000.000 6562.0000
## CV residual  3603.384 -2135.782 -1644.827 2392.202  2677.965 -816.0655
## 
## Sum of squares = 7723999018    Mean square = 21696626    n = 356 
## 
## Overall (Sum over all 356 folds) 
##       ms 
## 16902138

There are many other validation techniques and comparison charts that cannot be made automatically due to the nature of the categorical variables. The statistics above for our final model are satisfactory for our purposes.

Final Model and Summary

Again, the final model chosen to predict the price of an Airbnb Listing as below:

We found that bedrooms and host response rate had quite an influence model. However, while validating model after adding amenities the model was much better to predict and we decided to reject the inclusion of amenities to the model.

We hope this helps you gain a general expectation of the price you should be willing to pay given the type of listing and amenities you are looking for. Please reach out with your dream ideas and we can help you determine must-haves vs would-be-nice to find an Airbnb that meets your budget.

We wish you the best of luck on your Airbnb Listing!

AirBNBFinal_Project_BANA7038

Snehal Lokhande

2023-02-23